2025/03/24 by Poineau, Jérôme · 1 citation
#14A10 #14D06 #14G22 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2503.18643
Let X be an algebraic variety over C. We define a canonical compactification X \urcorner of the complex analytic space X(C) by adding a Berkovich space over a trivially valued field at the boundary. The construction is functorial with respect to proper morphisms and preserves many properties, such as normality, regularity, etc. We prove a partial GAGA theorem in this setting : there is an equivalence between the categories of coherent sheaves on X and X \urcorner, and it induces bijections on global sections. The results still hold if C is replaced by a complete non-trivially valued field k, and complex analytic spaces by Berkovich analytic spaces over k.